arxiv: 2605.11681 · v1 · submitted 2026-05-12 · 🧮 math.HO

Recognition: no theorem link

Diverse yet consistent: How mathematicians position computational thinking across research and teaching

Elise Lockwood, Jan-Fredrik Olsen, Tor Ole B Odden

Pith reviewed 2026-05-13 00:46 UTC · model grok-4.3

classification 🧮 math.HO

keywords computational thinkingmathematical thinkingmathematiciansteaching practicesresearch practicesintegrationperspectivesepistemic and ontological positioning

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The pith

Mathematicians integrate programming into teaching most readily when they tie it to real-world impact rather than treating theory as the sole authority.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The study interviews fifteen mathematicians at one institution with two decades of computation integration to map how they connect computational thinking with mathematical thinking in both research and teaching. It isolates three consistent perspectives: theory as the source of control, computation as a pragmatic extension of reach, and real-world applications as the source of legitimacy. These positions directly predict classroom choices, with real-world emphasis driving integration and theory-first views keeping computation at arm's length. The authors conclude that apparent clashes between the two ways of thinking are ontological, rooted in differing goals for mathematical work, rather than purely epistemic. This framing implies that meaningful combination in education depends on anchoring computation to purposes outside mathematics itself.

Core claim

Interviews reveal three perspectives that organize mathematicians' positioning of computation: mathematical theory viewed as a source of control, computations viewed as a source of pragmatic reach, and real-world impact viewed as a source of legitimacy. Mathematicians who stress real-world impact most readily carry programming into their teaching, while those who treat theoretical mathematics as authoritative are least likely to do so; researchers focused on numerical algorithms sit in an intermediate, uneasy position. The study argues that tensions between computational thinking and mathematical thinking are not solely about kinds of knowledge but about how computations are situated within

What carries the argument

The three-perspectives model, built from interview data, that classifies stances on computation according to their relation to theoretical control, pragmatic utility, and external legitimacy.

If this is right

Mathematicians prioritizing real-world legitimacy will embed programming more deeply in courses than those prioritizing theoretical control.
Numerical algorithm work creates ongoing tension between the three perspectives rather than fitting neatly into one.
Perceived clashes between computational and mathematical thinking can be reduced by shifting focus from knowledge types to the purposes of mathematical activity.
Integration stabilizes when courses tie computation to authentic goals drawn from outside pure mathematics.
Context shapes whether computational thinking feels like a natural extension of mathematical practice.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Professional development for mathematicians could explicitly surface these three perspectives to ease adoption of computation in teaching.
The model suggests curriculum designers should start with real-world projects rather than abstract programming exercises to increase uptake.
Future work could test whether the same three stances appear in other quantitative fields such as physics or engineering.
Generative AI may alter the pragmatic-reach perspective by lowering barriers to computation for theory-first mathematicians.

Load-bearing premise

The three perspectives drawn from interviews at one long-established computation-integrated site capture the main patterns across mathematicians in general.

What would settle it

Replicate the interview study at several institutions without a twenty-year history of computation integration and test whether the same three perspectives emerge with the same links to teaching practices.

read the original abstract

Recent research in mathematics education points to an "epistemic clash" when programming and computational thinking (CT) are leveraged alongside more established forms of mathematical thinking (MT). The emergence of generative AI emphasises the need to understand the mechanisms shaping relations between CT and MT. We address this need by analysing interviews with 15 mathematicians on their use of computations across their teaching and research activities. The interviews were conducted at a critical site with a history of integrating computations across its science and mathematics programs for more than 20 years. Drawing on Cultural Historical Activity Theory and Communities of Practice theory, we consider MT and CT as methodologies grounded in practice. We identify three perspectives shaping how mathematicians position CT: mathematical theory considered as a source of control, computations as a source of pragmatic reach, and real-world impact as a source of legitimacy. This three-perspectives model explains why mathematicians who emphasise real-world impact are most likely to carry programming into teaching, whereas those who position theoretical mathematics as authoritative are least likely to do so. Mathematicians working on numerical algorithms occupy an uneasy intermediate position. Our findings suggest that the perceived clash between MT and CT is not purely epistemic, but also ontological, as it depends on how computations are positioned within the goal of doing mathematics. For mathematics education, this implies that perceived meaningful integration with CT is mediated by context, and that more extensive use can be stabilised by leveraging authentic learning goals external to mathematics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Interviews at one computation-friendly department yield a three-perspectives model on CT positioning that ties to teaching integration, but the single-institution sample raises questions about broader reach.

read the letter

The paper's core contribution is a three-perspectives framework drawn from interviews with 15 mathematicians. It suggests that how people see computations—either as subordinate to mathematical theory, as a way to extend reach, or as a source of real-world legitimacy—shapes whether they bring programming into their courses. Those focused on real-world impact integrate most readily, theory-oriented ones least, and numerical work sits in the middle. It does a decent job framing mathematical thinking and computational thinking as practices using Cultural Historical Activity Theory and Communities of Practice. This moves past a simple epistemic clash to something more about goals and legitimacy in doing math. The link to teaching decisions is a reasonable extension from the data they describe. The main limitation is the sample. Everything comes from one institution with two decades of computation integration already in place. That history could shape the perspectives they found, making it hard to say if the model travels to other departments or subfields. The abstract gives no information on how the interviews were analyzed, what coding looked like, or how they arrived at the three perspectives, so the strength of the evidence is difficult to judge from what's here. This work would interest researchers in mathematics education who study computational thinking at the university level. Someone trying to understand or improve integration of programming in math courses might find the positioning idea useful as a starting point. I would recommend sending it for peer review. The ideas are worth testing against more data, and the framing is clear enough that referees could help strengthen the methods and scope.

Referee Report

2 major / 0 minor

Summary. The manuscript reports on a qualitative study involving interviews with 15 mathematicians at one institution known for long-standing integration of computations in its programs. Using Cultural Historical Activity Theory (CHAT) and Communities of Practice (CoP) frameworks, the authors identify three perspectives that shape how mathematicians position computational thinking (CT) in relation to mathematical thinking (MT): mathematical theory as a source of control, computations as a source of pragmatic reach, and real-world impact as a source of legitimacy. The resulting three-perspectives model is presented as explaining variations in the integration of programming into teaching, with those emphasizing real-world impact being most likely to do so and those prioritizing theoretical authority least likely, while those in numerical algorithms occupy an intermediate position. The paper argues that the perceived clash between MT and CT is ontological rather than purely epistemic and has implications for mathematics education.

Significance. Should the three-perspectives model prove robust and generalizable, this work would contribute meaningfully to mathematics education by providing a practice-based framework for understanding and addressing the integration of computational thinking into mathematical research and teaching. By highlighting how different positionings of computations affect teaching practices, it could guide efforts to make CT integration more meaningful and context-sensitive, particularly in light of advances in generative AI.

major comments (2)

The abstract provides no information on the data analysis methods, including coding procedures, how themes were derived, inter-rater reliability, or member checking. Without these details, it is difficult to assess the validity and reliability of the identified three perspectives and their associations with teaching practices.
The study is limited to 15 mathematicians at a single institution pre-selected for its 20-year history of computation integration. This raises concerns about generalizability; the explanatory power of the three-perspectives model for broader patterns in how mathematicians position CT and MT may be influenced by site-specific factors such as departmental culture or incentives, rather than representing general mechanisms.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the referee's detailed and constructive comments. We have carefully considered each point and provide our responses below, along with planned revisions to the manuscript.

read point-by-point responses

Referee: The abstract provides no information on the data analysis methods, including coding procedures, how themes were derived, inter-rater reliability, or member checking. Without these details, it is difficult to assess the validity and reliability of the identified three perspectives and their associations with teaching practices.

Authors: We concur that the abstract would benefit from additional methodological details to improve transparency and allow for better assessment of the findings. In the revised version, we will update the abstract to include a concise description of the data analysis: interviews were transcribed and analyzed using thematic analysis guided by the CHAT and CoP frameworks, with themes iteratively derived through open and axial coding. We will also note that member checking was conducted with participants and that the analysis involved discussion among the research team to ensure consistency. Full details remain in the methods section of the paper. This revision addresses the concern without altering the word count significantly. revision: yes
Referee: The study is limited to 15 mathematicians at a single institution pre-selected for its 20-year history of computation integration. This raises concerns about generalizability; the explanatory power of the three-perspectives model for broader patterns in how mathematicians position CT and MT may be influenced by site-specific factors such as departmental culture or incentives, rather than representing general mechanisms.

Authors: We appreciate this observation on the scope of the study. As a qualitative investigation, our primary goal is to generate theoretical insights rather than statistical generalizability. The selection of this particular institution was deliberate to examine a context where computational integration has been sustained over time, allowing us to identify nuanced positionings. However, we recognize that site-specific factors could influence the findings. In the revised manuscript, we will expand the limitations and future research sections to explicitly discuss potential influences of departmental culture and to propose multi-site studies for validating the three-perspectives model. This will clarify the intended contribution as a practice-based framework for further exploration. revision: yes

Circularity Check

0 steps flagged

No circularity in qualitative derivation from external theories

full rationale

The paper's central three-perspectives model is obtained by applying established external frameworks (Cultural Historical Activity Theory and Communities of Practice) to interview data from 15 mathematicians. No equations, fitted parameters, self-citations, or self-definitional reductions appear in the provided abstract or derivation chain; the explanatory link between perspectives and teaching practices is presented as an interpretive outcome of the analysis rather than a tautological renaming or prediction forced by the inputs themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the applicability of Cultural Historical Activity Theory and Communities of Practice theory to frame MT and CT as practice-based methodologies, plus the assumption that interview data from one site can reveal general positioning patterns.

axioms (1)

domain assumption Cultural Historical Activity Theory and Communities of Practice theory appropriately frame mathematical thinking and computational thinking as methodologies grounded in practice.
Explicitly invoked in the abstract to analyze how mathematicians position CT relative to MT.

invented entities (1)

Three-perspectives model (mathematical theory as source of control, computations as source of pragmatic reach, real-world impact as source of legitimacy) no independent evidence
purpose: To explain variation in mathematicians' integration of programming into teaching.
Derived from the 15 interviews; no external falsifiable evidence or independent validation is mentioned.

pith-pipeline@v0.9.0 · 5532 in / 1414 out tokens · 55735 ms · 2026-05-13T00:46:20.787831+00:00 · methodology